Thermoelectric magnetohydrodynamic flow in a liquid metal-infused trench

TL;DR

This paper develops a mathematical model and numerical simulations to analyze thermoelectric magnetohydrodynamic flow of liquid lithium in a trench, revealing how physical parameters influence flow and magnetic fields.

Contribution

It introduces a new combined analytical and numerical approach to study TEMHD flow in liquid metals within trench geometries, including asymptotic solutions for large Hartmann numbers.

Findings

Flow velocity depends on heat flux and magnetic field strength.

Magnetic field and temperature profiles are characterized for different parameters.

Asymptotic solutions match numerical results in the high Hartmann number limit.

Abstract

We derive a mathematical model for steady, unidirectional, thermoelectric magnetohydrodynamic (TEMHD) flow of liquid lithium along a solid metal trench, subject to an imposed heat flux. We use a finite-element method implemented in COMSOL Multiphysics to solve the problem numerically, demonstrating how the fluid velocity, induced magnetic field and temperature change depending on the key physical and geometrical parameters. The observed flow structures are elucidated by using the method of matched asymptotic expansions to obtain approximate solutions in the limit where the Hartmann number is large and the trench walls are thin.